Heeke Eigenforms in the Cohomology of Congruence Subgroups of SL(3, Z)

Hecke Eigenforms in the Cohomology of Congruence Subgroups of SL(3, ZZ)

Galois representations from the cohomology of SL(3, Z)

Ash's research was partially supported by NSF Grant DMS-8919696. Conjecturally, any “algebraic” automorphic representation on GL(n) should have an n-dimensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology overC of congruence subgroups of GL(n;Z). On the other hand, the first author has conjectured that for any Hecke eigenclass ...

Cohomology of congruence subgroups of SL(4,Z) II

In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212] we computed cohomology groups H (Γ0(N),C), where Γ0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N . In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and addi...

Torsion in the Cohomology of Congruence Subgroups of Sl(4,z) and Galois Representations

We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4, Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computatio...

On the homology of congruence subgroups and k(3)(z).

Let Gamma(n;p) be the congruence subgroup of SL(n;Z) of level p. We study the homology and cohomology of Gamma(n;p) as modules over SL(n;F(p)) and apply our results to obtain an upper bound for the order of K(3)(Z).